Properties

Label 182.2.d
Level 182
Weight 2
Character orbit d
Rep. character \(\chi_{182}(155,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 2
Sturm bound 56
Trace bound 1

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Defining parameters

Level: \( N \) = \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 182.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(56\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(182, [\chi])\).

Total New Old
Modular forms 32 8 24
Cusp forms 24 8 16
Eisenstein series 8 0 8

Trace form

\( 8q - 8q^{4} + 20q^{9} + O(q^{10}) \) \( 8q - 8q^{4} + 20q^{9} - 8q^{10} - 16q^{13} + 4q^{14} + 8q^{16} - 8q^{17} + 4q^{22} + 12q^{23} - 16q^{25} - 24q^{27} + 16q^{29} + 8q^{30} - 20q^{36} - 16q^{38} + 8q^{40} + 4q^{42} + 24q^{43} - 8q^{49} - 8q^{51} + 16q^{52} - 8q^{53} + 40q^{55} - 4q^{56} - 16q^{61} + 24q^{62} - 8q^{64} - 12q^{65} - 32q^{66} + 8q^{68} + 16q^{69} + 12q^{74} - 80q^{75} - 24q^{77} - 44q^{78} - 44q^{79} + 48q^{81} + 40q^{82} + 88q^{87} - 4q^{88} + 32q^{90} + 8q^{91} - 12q^{92} + 8q^{94} + 24q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(182, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
182.2.d.a \(2\) \(1.453\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}+2iq^{5}-iq^{6}+\cdots\)
182.2.d.b \(6\) \(1.453\) 6.0.30647296.1 None \(0\) \(2\) \(0\) \(0\) \(q+\beta _{4}q^{2}+\beta _{3}q^{3}-q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(182, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(182, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{3} \))
$3$ (\( ( 1 + T + 3 T^{2} )^{2} \))(\( ( 1 - T - T^{2} + 8 T^{3} - 3 T^{4} - 9 T^{5} + 27 T^{6} )^{2} \))
$5$ (\( ( 1 - 4 T + 5 T^{2} )( 1 + 4 T + 5 T^{2} ) \))(\( 1 - 6 T^{2} + 11 T^{4} - 44 T^{6} + 275 T^{8} - 3750 T^{10} + 15625 T^{12} \))
$7$ (\( 1 + T^{2} \))(\( ( 1 + T^{2} )^{3} \))
$11$ (\( 1 + 3 T^{2} + 121 T^{4} \))(\( 1 - T^{2} + 251 T^{4} - 198 T^{6} + 30371 T^{8} - 14641 T^{10} + 1771561 T^{12} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 + 10 T + 61 T^{2} + 256 T^{3} + 793 T^{4} + 1690 T^{5} + 2197 T^{6} \))
$17$ (\( ( 1 + 2 T + 17 T^{2} )^{2} \))(\( ( 1 + 2 T + 7 T^{2} + 12 T^{3} + 119 T^{4} + 578 T^{5} + 4913 T^{6} )^{2} \))
$19$ (\( 1 - 22 T^{2} + 361 T^{4} \))(\( 1 - 86 T^{2} + 3451 T^{4} - 82508 T^{6} + 1245811 T^{8} - 11207606 T^{10} + 47045881 T^{12} \))
$23$ (\( ( 1 - 9 T + 23 T^{2} )^{2} \))(\( ( 1 + 3 T + 53 T^{2} + 106 T^{3} + 1219 T^{4} + 1587 T^{5} + 12167 T^{6} )^{2} \))
$29$ (\( ( 1 + 29 T^{2} )^{2} \))(\( ( 1 - 8 T + 67 T^{2} - 288 T^{3} + 1943 T^{4} - 6728 T^{5} + 24389 T^{6} )^{2} \))
$31$ (\( 1 - 37 T^{2} + 961 T^{4} \))(\( 1 - 121 T^{2} + 7651 T^{4} - 293638 T^{6} + 7352611 T^{8} - 111746041 T^{10} + 887503681 T^{12} \))
$37$ (\( 1 - 65 T^{2} + 1369 T^{4} \))(\( 1 - 157 T^{2} + 11771 T^{4} - 540558 T^{6} + 16114499 T^{8} - 294243277 T^{10} + 2565726409 T^{12} \))
$41$ (\( 1 - 57 T^{2} + 1681 T^{4} \))(\( 1 - 133 T^{2} + 8499 T^{4} - 385678 T^{6} + 14286819 T^{8} - 375826213 T^{10} + 4750104241 T^{12} \))
$43$ (\( ( 1 - 4 T + 43 T^{2} )^{2} \))(\( ( 1 - 8 T + 105 T^{2} - 560 T^{3} + 4515 T^{4} - 14792 T^{5} + 79507 T^{6} )^{2} \))
$47$ (\( 1 + 75 T^{2} + 2209 T^{4} \))(\( 1 - 137 T^{2} + 8067 T^{4} - 352934 T^{6} + 17820003 T^{8} - 668516297 T^{10} + 10779215329 T^{12} \))
$53$ (\( ( 1 - 14 T + 53 T^{2} )^{2} \))(\( ( 1 + 6 T + 53 T^{2} )^{6} \))
$59$ (\( 1 - 82 T^{2} + 3481 T^{4} \))(\( 1 - 66 T^{2} + 10763 T^{4} - 439844 T^{6} + 37466003 T^{8} - 799745826 T^{10} + 42180533641 T^{12} \))
$61$ (\( ( 1 + 13 T + 61 T^{2} )^{2} \))(\( ( 1 - 5 T + 181 T^{2} - 608 T^{3} + 11041 T^{4} - 18605 T^{5} + 226981 T^{6} )^{2} \))
$67$ (\( 1 - 125 T^{2} + 4489 T^{4} \))(\( 1 - 289 T^{2} + 39707 T^{4} - 3327366 T^{6} + 178244723 T^{8} - 5823673969 T^{10} + 90458382169 T^{12} \))
$71$ (\( ( 1 - 71 T^{2} )^{2} \))(\( 1 - 90 T^{2} + 12959 T^{4} - 845804 T^{6} + 65326319 T^{8} - 2287051290 T^{10} + 128100283921 T^{12} \))
$73$ (\( 1 - 145 T^{2} + 5329 T^{4} \))(\( 1 - 349 T^{2} + 54115 T^{4} - 4959166 T^{6} + 288378835 T^{8} - 9910986109 T^{10} + 151334226289 T^{12} \))
$79$ (\( ( 1 + 15 T + 79 T^{2} )^{2} \))(\( ( 1 + 7 T + 149 T^{2} + 1254 T^{3} + 11771 T^{4} + 43687 T^{5} + 493039 T^{6} )^{2} \))
$83$ (\( 1 - 130 T^{2} + 6889 T^{4} \))(\( 1 - 146 T^{2} + 27387 T^{4} - 2110724 T^{6} + 188669043 T^{8} - 6928914866 T^{10} + 326940373369 T^{12} \))
$89$ (\( 1 - 142 T^{2} + 7921 T^{4} \))(\( 1 - 218 T^{2} + 26655 T^{4} - 2647148 T^{6} + 211134255 T^{8} - 13677808538 T^{10} + 496981290961 T^{12} \))
$97$ (\( 1 - 145 T^{2} + 9409 T^{4} \))(\( 1 - 397 T^{2} + 77507 T^{4} - 9352542 T^{6} + 729263363 T^{8} - 35146124557 T^{10} + 832972004929 T^{12} \))
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